Sequentially Cohen-Macaulay monomial ideals of embedding dimension four

Details Sequentially Cohen-Macaulay monomial ideals of embedding dimension four Sequentially Cohen-Macaulay monomial ideals of embedding dimension four

2007-02-20

arxiv.org/abs/math/0702569v2

Mathematics

Commutative Algebra

11 pages

Scientific paper

Let $I$ be a monomial ideal of the polynomial ring $S=K[x_1,...,x_4]$ over a
field $K$. Then $S/I$ is sequentially Cohen-Macaulay if and only if $S/I$ is
pretty clean. In particular, if $S/I$ is sequentially Cohen-Macaulay then $I$
is a Stanley ideal.

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